What is the integral of (3x+15)sqrt(x^2+10x+4) ?

The integral of (3x+15)sqrt(x^2+10x+4) is (x^2+10x+4)^{3/2}+C

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integral of (3x+15)sqrt(x^2+10x+4)

\int (3 x + 15) x^{2} + 10 x + 4 d x

(x^{2} + 10 x + 4)^{\frac{3}{2}} + C

Solution steps

\int (3 x + 15) x^{2} + 10 x + 4 d x

Apply u-substitution

: \int \frac{3 u}{2} d u

= \int \frac{3 u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{3}{2} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{3}{2} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x^{2} + 10 x + 4

= \frac{3}{2} \cdot \frac{2}{3} (x^{2} + 10 x + 4)^{\frac{3}{2}}

Simplify

\frac{3}{2} \cdot \frac{2}{3} (x^{2} + 10 x + 4)^{\frac{3}{2}} : (x^{2} + 10 x + 4)^{\frac{3}{2}}

= (x^{2} + 10 x + 4)^{\frac{3}{2}}

Add a constant to the solution

= (x^{2} + 10 x + 4)^{\frac{3}{2}} + C

\int (e^{2 t}) d t

\frac{sin ( 3 x )}{tan ( 4 x )}

\frac{1}{x - 1}, 21

f (x) = e^{x} (tan (x) - x)

\int_{0}^{\frac{1}{6}} \frac{3}{1 - 9 x ^{2}} d x

What is the integral of (3x+15)sqrt(x^2+10x+4) ?
The integral of (3x+15)sqrt(x^2+10x+4) is (x^2+10x+4)^{3/2}+C